Gabriel Molina-Terriza

Duality symmetry and Kerker conditions

We unveil the relationship between two anomalous scattering processes known as Kerker conditions and the duality symmetry of Maxwell equations. We generalize these conditions and show that they can be applied to any particle with cylindrical symmetry, not only to spherical particles as the original Kerker conditions were derived for. We also explain the role of the optical helicity in these scattering processes. Our results find applications in the field of metamaterials, where new materials with directional scattering are being explored.

How a Dove prism transforms the orbital angular momentum of a light beam

It is generally assumed that a light beam with orbital angular momentum (OAM) per photon of lh, is transformed, when traversing a Dove prism, into a light beam with OAM per photon of -lh. In this paper, we show theoretically and experimentally that this OAM transformation rule does not apply for highly focused light beams. This result should be taken into account when designing classical and quantum algorithms that make use of Dove prims to manipulate the OAM of light.

Excitation of single multipolar modes with engineered cylindrically symmetric fields

We present a new method to address multipolar resonances and to control the scattered field of a spherical scatterer. This method is based on the engineering of the multipolar content of the incident beam. We propose experimentally feasible techniques to generate light beams which contain only a few multipolar modes. The technique uses incident beams with a well defined component of the angular momentum and appropriate focusing with aplanatic lenses. The control of the multipolar content of light beams allow for the excitation of single Mie resonances and unprecedented control of the scattered field from spherical particles.

Dual and anti-dual modes in dielectric spheres

We present how the angular momentum of light can play an important role to induce a dual or anti-dual behaviour on a dielectric particle. Although the material the particle is made of is not dual, i.e. a dielectric does not interact with an electrical field in the same way as it does with a magnetic one, a spherical particle can behave as a dual system when the correct excitation beam is chosen. We study the conditions under which this dual or anti-dual behaviour can be induced.

The role of the angular momentum of light in Mie scattering. Excitation of dielectric spheres with Laguerre-Gaussian modes

We present a method to enhance the ripple structure of the scattered electromagnetic field in the visible range through the use of Laguerre–Gaussian beams. The position of these enhanced ripples as well as their linewidths can be controlled using different optical beams and sizes of the spheres.

Correcting vortex splitting in higher order vortex beams

We demonstrate a general method for the first order compensation of singularity splitting in a vortex beam at a single plane. By superimposing multiple forked holograms on the SLM used to generate the vortex beam, we are able to compensate vortex splitting and generate beams with desired phase singularities of order ℓ = 0, 1, 2, and 3 in one plane. We then extend this method by application of a radial phase, in order to simultaneously compensate the observed vortex splitting at two planes (near and far field) for an ℓ = 2 beam.

Characterization of dielectric spheres by spiral imaging

We study the spiral spectra scattered off transparent dielectric spheres when probed by different Laguerre-Gaussian light beams, carrying nested topological wavefront dislocations. We show that such scattering data may be employed to determine geometrical properties of the spheres, such as their position. The technique is a generalization of standard Mie scattering, and it can be extended to study and to characterize nanospheres.

Orbital angular momentum correlations of entangled paired photons

The generation of paired photons entangled in the spatial degree of freedom, i.e., in orbital angular momentum, offers a convenient physical resource to investigate the nature of entanglement in a multidimensional Hilbert space with controllable dimensionality. The two main physical processes that generate pairs of photons which show correlations in orbital angular momentum are (a) spontaneous parametric down-conversion (SPDC), and (b) Raman transitions induced in atomic ensembles. One question naturally arises: what kinds of correlations exist between the orbital angular momentum of the generated photons? The answer might be different if we consider the whole quantum state of the generated photons, i.e., all possible directions where the pairs of photons can be emitted, or if we consider only a small section of the full set of directions.

On the transformations generated by the electromagnetic spin and orbital angular momentum operators

We present a study of the properties of the transversal “spin angular momentum” and “orbital angular momentum” operators. We show that the “spin angular momentum” operators are generators of spatial translations that depend on helicity and frequency and that the “orbital angular momentum” operators generate transformations that are a sequence of this kind of translation and rotation. We give some examples of the use of these operators in light–matter interaction problems. Their relationship with the helicity operator allows us to involve electromagnetic duality symmetry in the analysis. We also find that simultaneous eigenstates of the three “spin” operators and parity define a type of standing mode that has recently been singled out for the interaction of light with chiral molecules. With respect to the relationship between “spin angular momentum,” polarization, and total angular momentum, we show that, except for the case of a single plane wave, the total angular momentum of the field is decoupled from its vectorial degrees of freedom even in the regime in which the paraxial approximation holds. Finally, we point out a relationship between the three “spin” operators and the spatial part of the Pauli–Lubanski four vector.

Measurement and limitations of optical orbital angular momentum through corrected atmospheric turbulence.

In recent years, there have been a series of proposals to exploit the orbital angular momentum (OAM) of light for astronomical applications. The OAM of light potentially represents a new way in which to probe the universe. The study of this property of light entails the development of new instrumentation and problems which must be addressed. One of the key issues is whether we can overcome the loss of the information carried by OAM due to atmospheric turbulence. We experimentally analyze the effect of atmospheric turbulence on the OAM content of a signal over a range of realistic turbulence strengths typical for astronomical observations. With an adaptive optics system we are able to recover up to 89% power in an initial non-zero OAM mode (ℓ = 1) at low turbulence strengths (0.30 FWHM seeing). However, for poorer seeing conditions (1.1 FWHM seeing), the amount of power recovered is significantly lower (5%), showing that for the terrestrial detection of astronomical OAM, a careful design of the adaptive optics system is needed.